$$  $$Evaluate the following expression. Enter your answer as an integer or a simplified fraction.  6$$ ^{-4} $$

The expression you want to evaluate is $ 6^{-4} $.

To evaluate this, recall that a negative exponent means taking the reciprocal of the base and then raising it to the positive exponent. In this case:

\[
6^{-4} = \frac{1}{6^4}
\]

Now, calculate $ 6^4 $:

\[
6^4 = 6 \times 6 \times 6 \times 6 = 1296
\]

So:

\[
6^{-4} = \frac{1}{1296}
\]

Thus, the simplified result is:

\[
6^{-4} = \frac{1}{1296}
\]

Would you like any more details or have any questions? Here are some related questions you might want to explore:

1. What is $ 7^{-3} $?
2. How do you simplify $ 5^{-2} $?
3. What happens when you have a negative exponent with a fraction as the base?
4. How would you evaluate $ 2^{-5} $?
5. What is the reciprocal of $ 9^3 $?

**Tip:** A negative exponent tells you to "flip" the base and make the exponent positive!

Evaluate the following expression. Enter your answer as an integer or a simplified fraction. 6^{-4}

Learn how to evaluate the expression 6^-4 with a detailed step-by-step solution. This problem covers key mathematical concepts such as exponents and negative exponents, using the negative exponent rule. Suitable for students in Grades 6-8.

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